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The components for proper motion in the equatorial coordinate system (of a given epoch, often J2000.0) are given in the direction of right ascension (μ α) and of declination (μ δ). Their combined value is computed as the total proper motion (μ). [2] [3] It has dimensions of angle per time, typically arcseconds per year or milliarcseconds ...
English: Components of proper motion on the Celestial sphere. The celestial north pole is CNP, the vernal equinox is V, the star path on the celestial sphere is indicated by arrows. The proper motion vector is μ, α = right ascension, δ = declination, θ = position angle.
There is no specific velocity that is considered high, but the proper motion article notes that the majority of stars have a proper motion of 0.01 arc-seconds per year. Note that the closer a star is to earth, the faster it will appear to travel in arc-seconds per year for a given "real" velocity; therefore, the PM values here are apparent ...
Log-log plot of γ (blue), v/c (cyan), and η (yellow) versus proper velocity w/c (i.e. momentum p/mc).Note that w/c is tracked by v/c at low speeds and by γ at high speeds. The dashed red curve is γ − 1 (kinetic energy K/mc 2), while the dashed magenta curve is the relativistic Doppler factor.
The transverse, or proper motion must be found by taking a series of positional determinations against more distant objects. Once the distance to a star is determined through astrometric means such as parallax, the space velocity can be computed. [2] This is the star's actual motion relative to the Sun or the local standard of rest (LSR).
On this usage, comoving and proper distances are numerically equal at the current age of the universe, but will differ in the past and in the future; if the comoving distance to a galaxy is denoted , the proper distance () at an arbitrary time is simply given by = where () is the scale factor (e.g. Davis & Lineweaver 2004). [2]
Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.
Orbital position vector, orbital velocity vector, other orbital elements. In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position and velocity that together with their time () uniquely determine the trajectory of the orbiting body in space.